hw4 - 16.31 Prof J P How T.A TBD Handout#5 Due October 5...

16.31 Handout #5 Prof. J. P. How September 28, 2007 T.A. TBD Due: October 5, 2007 16.31 Homework Assignment #4 1. The goal is to design an autopilot for the altitude dynamics of an airplane. Overall, the only important dynamics are the long period (phugoid) motion, which gives the transfer function from elevator input to height output of h ( s ) 15( s + 0 . 01) = δ e ( s ) s ( s 2 + 0 . 01 s + 0 . 002) The input to the autopilot also includes the desired height h c , resulting in the error e ( s ) = h c ( s ) − h ( s ), and δ e ( s ) = G c ( s ) e ( s ). (a) Use Matlab to obtain the Bode plot of this system. Choose a constant so that with G c ( s ) = K , the system has a crossover frequency of 0.15 rad/sec. For this value of K would the system be stable, if so, what are the gain and phase margins? (b) For your design, what would be the steady-state error if the command was a ramp at 3 ft/sec? (c)

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